An easy fix to that is an old trick we used to use when we glassed pattern airplane wings back in the old days. Spray a LIGHT coat of hairspray onto the wings before you glass. This will seal the wood just a bit and prevent so much resin from being soaked in.
Yeah, I've actually done that, what I ended up doing was actually mixing some talc into the resin, filled the weave nicely and didn't soak up so much resin, but the main problem isn't really the soaking up, it's the very open grain of the obechi leaving grain lines in the resin for the first couple coats. The talc just acted as a filler. Worked out well.
I flew pattern for quite a while, but used ultracote on all the flight surfaces, just a little lighter, I miss my pattern birds, might have to do another one someday